Analysis of Passive Walking Gait and Non-Synchronization of Combined Flexible Legged Rimless Wheels

WANG Longyu; ZHANG Qizhi; LI Shanshan

doi:10.21656/1000-0887.450182

Volume 46 Issue 9

Sep. 2025

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Article Navigation > Applied Mathematics and Mechanics > 2025 > 46(9): 1158-1175

WANG Longyu, ZHANG Qizhi, LI Shanshan. Analysis of Passive Walking Gait and Non-Synchronization of Combined Flexible Legged Rimless Wheels[J]. Applied Mathematics and Mechanics, 2025, 46(9): 1158-1175. doi: 10.21656/1000-0887.450182

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Analysis of Passive Walking Gait and Non-Synchronization of Combined Flexible Legged Rimless Wheels

doi: 10.21656/1000-0887.450182

1. School of Automation, Beijing Information Science & Technology University, Beijing 100192, P.R.China;
2. School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, P.R.China

Funds:

The National Science Foundation of China(12172059)

Received Date: 2024-06-21
Rev Recd Date: 2024-10-22

Available Online: 2025-10-17

Abstract

Abstract

A combined flexible-legged rimless wheels model with variable phase difference was introduced for the analysis of passive walking gait by adjusting the initial value of the system. The model’s motions under various phase differences were simulated, and the effects of phase differences on the walking gait were investigated. Firstly, the 2nd-type Lagrangian method was used to establish a dynamic model for combined flexible legged rimless wheels with variable phase differences, and the initial value was adjusted to gradually form the convergent closed-loop limit cycle for the model motion gait under various phase differences. Secondly, the typical model gaits were simulated and comparatively analyzed to expose the close relationship between the model walking gait and the initial phase difference, which were verified through numerical experiments. The results show that, the variation of the phase differences between the rimless wheel support legs before and after the initial moments change the model periodical motion gait on the inclined plane. With a phase difference close to the half hip angle, the model average moving speed along the inclined plane will decrease, while the bump motion perpendicular to the inclined plane will be relatively small, and the maximum reverse support force in the normal direction of the inclined plane will also be relatively small.
- combined flexible legged rimless wheels,
- passive walking,
- phase difference speed regulation,
- non-synchronization,
- limit cycle

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References(21)

References

MCGEER T. Passive dynamic walking[J]. The International Journal of Robotics Research,1990,9(2): 62-82.

[2]BLICKHAN R. The spring-mass model for running and hopping[J]. Journal of Biomechanics,1989,22(11/12): 1217-1227.

[3]VISSER L C, STRAMIGIOLI S, CARLONI R. Robust bipedal walking with variable leg stiffness[C]//2012 4th IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics (BioRob). Rome, Italy. IEEE, 2012: 1626-1631.

[4]SMITH A C, BERKEMEIER M D. Passive dynamic quadrupedal walking[C]//Proceedings of International Conference on Robotics and Automation. Albuquerque, NM, USA: IEEE, 1997: 34-39.

[5]REMY C D, BUFFINTON K, SIEGWART R. Stability analysis of passive dynamic walking of quadrupeds[J]. The International Journal of Robotics Research,2010,29(9): 1173-1185.

[6]NAKATANI K, SUGIMOTO Y, OSUKA K. Demonstration and analysis of quadrupedal passive dynamic walking[J]. Advanced Robotics,2009,23(5): 483-501.

[7]ASANO F. Stealth walking with reduced double-limb support phase and its extension to careful legged locomotion[J]. Multibody System Dynamics,2018,44(4): 421-447.

[8]ASANO F, TOKUDA I. Indirectly controlled limit cycle walking of combined rimless wheel based on entrainment to active wobbling motion[J]. Multibody System Dynamics,2015,34: 191-210.

[9]ASANO F, KAWAMOTO J. Modeling and analysis of passive viscoelastic-legged rimless wheel that generates measurable period of double-limb support[J]. Multibody System Dynamics,2014,31: 111-126.

[10]王奇, 朱寅鑫, 牛培行, 等. 柔性扑翼翼型的气动性能仿真分析[J]. 应用数学和力学, 2022,43(5): 586-596.(WANG Qi, ZHU Yinxin, NIU Peixing, et al. Simulation of aerodynamic performances of flexible flapping wing airfoils[J]. Applied Mathematics and Mechanics,2022,43(5): 586-596.(in Chinese))

[11]MIYAMOTO H, IKEMATA Y, SANO A, et al. Passive running of rimless wheel with springs[C]//Mobile Robotics- Solutions and Challenges: The Twelfth International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines. Istanbul, Turkey： WORLD SCIENTIFIC, 2010: 269-276.

[12]SKIBBE J. Analysis of phase shifts for a rimless wheel rover[C]//2021 IEEE Aerospace Conference (50100). Big Sky, MT, USA： IEEE, 2021: 1-7.

[13]BUTTERFIELD J K, SIMHA S N, DONELAN J M, et al. The split-belt rimless wheel[J]. The International Journal of Robotics Research,2022,41(11/12): 1043-1076.

[14]IWATANI Y. Dynamics of rimless wheel robots during collision[J]. SICE Journal of Control,Measurement,and System Integration,2022,15(1): 1-9.

[15]IWATANI Y, TAKEI T. Steady locomotion in torso-actuated rimless wheel robots[J]. SICE Journal of Control,Measurement,and System Integration,2022,15(2): 99-108.

[16]何昊然, 张奇志, 周亚丽. 平面被动粘弹性腿无缘轮的动力学建模及步态分析[J]. 北京信息科技大学学报(自然科学版), 2023,38(4): 1-8.(HE Haoran, ZHANG Qizhi, ZHOU Yali. Dynamic modeling and gait analysis of planar passive viscoelastic-legged rimless wheel[J]. Journal of Beijing Information Science & Technology University,2023,38(4): 1-8.(in Chinese))

[17]陈伟, 张奇志, 周亚丽. 组合弹性无缘轮半被动行走的混沌和同步分析[J]. 力学季刊, 2024,45(1): 132-143.(CHEN Wei, ZHANG Qizhi, ZHOU Yali. Chaos and synchronization analysis of semi-passive walking of combined elastic rimless wheels[J]. Chinese Quarterly of Mechanics,2024,45(1): 132-143.(in Chinese))

[18]包晏名, 张奇志, 周亚丽. 柔性腿无缘轮黏滞-滑动过程的被动动态行走运动特性分析[J]. 动力学与控制学报, 2024,22(7): 59-69.(BAO Yanming, ZHANG Qizhi, ZHOU Yali. Analysis of the kinematic characteristics of the passive dynamic walking stick-slip process of the flexible leg rimless wheel[J]. Journal of Dynamics and Control,2024,22(7): 59-69.(in Chinese))

[19]李光伟, 杨旗, 牛金辉, 等. 四足机器人倾斜平面运动稳定控制研究[J]. 机械工程与自动化, 2024(5): 1-4.(LI Guangwei, YANG Qi, NIU Jinhui, et al. Research on stability control of tilting plane motion of quadruped robot[J]. Mechanical Engineering & Automation,2024(5): 1-4.(in Chinese))

[20]TANAKA D, ASANO F, TOKUDA I. Gait analysis and efficiency improvement of passive dynamic walking of combined rimless wheel with wobbling mass[C]//2012 IEEE/RSJ International Conference on Intelligent Robots and Systems. Vilamoura-Algarve, Portugal: IEEE, 2012: 151-156.

[21]张奇志, 周亚丽. 机器人学简明教程[M]. 西安: 西安电子科技大学出版社, 2013.（ZHANG Qizhi, ZHOU Yali. A Concise Guide to Robotics[M]. Xi’an: Xidian University Press, 2013. (in Chinese)）

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